Camila needs to fix the window on the front of her house. The bottom window is 16 feet from the ground. She only has a 20 feet ladder. How far from the base of the house should she set the ladder exactly so she can fix the bottom window?
To figure out how far from the base of the house Camila should set the ladder, we need to use the Pythagorean theorem. The ladder acts as the hypotenuse of a right triangle, with the ground distance as one leg and the height of the window as the other leg.
Let's label the distance from the base of the house to the ladder as 'x'. Using the Pythagorean theorem, we can write the equation: x^2 + 16^2 = 20^2.
Simplifying this equation:
x^2 + 256 = 400
x^2 = 400 - 256
x^2 = 144.
Taking the square root of both sides of the equation, we find that x = 12.
Therefore, Camila should set the ladder 12 feet from the base of the house to fix the window.
To find the distance from the base of the house where Camila should set the ladder, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
In this case, the ladder represents the hypotenuse, and the distance from the base of the house to the bottom window is one of the shorter sides.
Using the Pythagorean theorem, we can calculate the distance as follows:
Let the distance from the base of the house to the ladder be 'x.'
Using the Pythagorean theorem, we have:
(x^2) + (16^2) = (20^2)
Simplifying the equation:
x^2 + 256 = 400
Subtracting 256 from both sides of the equation:
x^2 = 144
Taking the square root of both sides of the equation:
x = √144
x = 12
Therefore, Camila should set the ladder 12 feet from the base of the house in order to fix the bottom window.
To determine where Camila should place the ladder, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder represents the hypotenuse of a right triangle, the height of the house (16 feet) represents one side, and the distance from the base of the ladder to the house represents the other side. Let's call this distance x.
Using the Pythagorean Theorem, we can set up the equation:
x^2 + 16^2 = 20^2
Simplifying the equation:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 144
Taking the square root of both sides:
x = √144
x = 12 feet
Therefore, Camila should place the ladder exactly 12 feet from the base of the house to fix the bottom window.